Abstract
The present work focus on water boundary layer flow over an exponential permeable stretching sheet in the presence of suction/injection with variable viscosity and prandtl number. The nonlinear partial differential equations governing flow and thermal fields are presented in non-dimensional form using suitable non-similar transformation. Finally non dimensional partial differential the equations are solved by the implicit finite difference method in combination with the Quasi-linearization technique. The numerical results for skin-friction and local Nusselt number are shown graphically to display effects of physical parameters.
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Abbreviations
- Pr :
-
Prandtl number
- f :
-
Dimensionless streamfunction
- \(C_{p}\) :
-
Specific heat at constant pressure
- T :
-
Temperature
- g :
-
Acceleration due to gravity
- \(U_{W}\) :
-
Moving plate velocity
- \(Nu_{x}\) :
-
Nusselt number
- \(Cf_{x}\) :
-
Skin friction coefficient
- \(U_{\infty }\) :
-
Free stream velocity
- v :
-
Velocity component in the y direction
- u :
-
Velocity component in the x direction
- \(\nu \) :
-
Kinematic viscosity
- \(\rho \) :
-
Density
- x, y:
-
Cartesian coordinates
- \(Re_{L}\) :
-
Local Reynolds number
- \(\mu \) :
-
Dynamic viscosity
References
ElbElbashbeshy, E.M.A.: Heat transfer over an exponentially stretching continuous surface with suction. Arch. Mech. 53, 643–651 (2001)
Zaimi, K., Ishak, A.: Boundary layer flow and heat transfer over a permeable stretching /shrinking sheet with convective boundary condition. J. Appl. Fluid Mech. 8, 499–505 (2015)
Naramgari, S., Sulochana, C.: MHD flow over a permeable stretching sheet of a nanofluid with suction/injection. Alexandria Eng. J. 55, 819–827 (2016)
Hafidzuddin, E.H., Nazar, R., Arifin, N.M., Pop, I.: Boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity. J. Appl. Fluid Mech. 9, 2025–2036 (2016)
Ishak, I., Nazar, R., Pop, I.: The effects of transpiration on the flow and heat transfer over a moving permeable surface in a parallel stream, chem. Eng. J. 148, 63–67 (2009)
Patil, P.M., Latha, D.N., Roy, S., Momoniat, E.: Non similar solutions of mixed convection flow from an exponentially stretching surface. Ain Shams Eng. J. 8, 697–705 (2015)
Olusoji, E.: Heat and mass transfer in MHD micropolar fluid flow over a stretching sheet with velocity and thermal slip conditions (2018)
Hayat, T., Imtiaz, M., Alsaedi, A.: MHD flow of Nanofluid over permeable stretching sheet with convective boundary conditions. Open J. Fluid Dyn. 8(2), 195 (2014)
Srinvasulu, T., Bandari, Shankar: MHD boundary layer flow of nanofluid over a nonlinear stretching sheet with effect of non-uniform heat source and chemical reaction. J. Nanofluids 6(4), 637–646 (2017)
Hayat, T., Shafiq, A., Alsaedi, A., Shahzad, S.A.: Unsteady MHD flow over exponentially stretching sheet with slip conditions. Appl. Math. Mech. 37(2), 193–208 (2016)
Bidin, Biliana, Nazar, Roslinda: Numerical solution of the boundary layer flow over an exponentially stretching sheet with thermal radiation. Eur. J. Sci. Res. 33, 710–717 (2009)
Cortel, R.: Fluid flow and radiative non linear heat transfer over a stretching sheet. J. King Saud Univ. Sci. 26, 161–167 (2014)
Singh, P.J., Roy, S., Pop, I.: Unsteady mixed convection from a rotating vertical slender cylinder in an axial flow. Int. J. Heat Mass Transf. 51, 1423–1430 (2008)
Tsou, F.K., Sparrow, E.M., Goldstein, R.J.: Flow and heat transfer in the boundary layer on a continuous moving surface. Int. Heat Mass Transfer 10, 219–235 (1967)
Soundalgekar, V.M., Murty, T.V.R.: Heat transfer in flow past a continuous moving plate with variable temperature. Warme-und Stoffubertragung 14, 91–93 (1980)
Ali, M.E.: On thermal boundary layer on a power-law stretched surface with suction or injection. Int. J. Heat Fluid Flow 16, 280–290 (1995)
Moutsoglou, T.S.Chen: Buoyancy effects in boundary layers on inclined, continuous, moving sheets. ASME J. Heat Transf. 102, 371–373 (1980)
Chen, C.H.: Laminar mixed convection adjacent to vertical, continuously stretching sheets. Heat Mass Transf. 33, 471–476 (1998)
Varga, R.S.: Matrix Itrative Analysis. Prentice-Hall, Englewood Cliffs, NJ (2000)
Tsou, F.K., Sparrow, E.M., Goldstein, R.J.: Flow and heat transfer in the boundary layer on a continuous moving surface. Int. J. Heat Mass Transf. 10, 219–235 (1967)
Moutsoglou, A., Chen, T.S.: Buoyancy effects in boundary layers on inclined continuous moving sheets. ASME J. Heat Transf. 102, 371–373 (1980)
Chen, C.H.: Laminar mixed convection adjacent to vertical continuously stretching sheets. Heat Mass Transf. 33, 471–476 (1998)
Lide, D.R. (ed.): CRC Handbook of Chemistry and Physics, 71st edn. CRC Press, BocaRaton, FL (1990)
Acknowledgements
Let me thanks organization team of International Conference on Mathematical Modelling and Scientific Computing who brought the platform to express our idea about mathematical modelling and simulation in applied mathematics. The current work is completely based on modelling of fluid dynamics problem and solution has been obtained by using finite difference method and given in terms of velocity profile (F), temperature profile \((\theta )\), skin friction coefficient \((C_{fx} \left( Re_L\xi exp({\xi })\right) ^{1/2})\) and heat transfer coefficients \((Nu_x (Re_L\xi exp({\xi }))^{-1/2})\).
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Singh, A.K., Govindaraj, N., Roy, S. (2020). Water Boundary Layer Flow over an Exponentially Permeable Stretching Sheet with Variable Viscosity and Prandtl Number. In: Manna, S., Datta, B., Ahmad, S. (eds) Mathematical Modelling and Scientific Computing with Applications. ICMMSC 2018. Springer Proceedings in Mathematics & Statistics, vol 308. Springer, Singapore. https://doi.org/10.1007/978-981-15-1338-1_16
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